I understand PT 11 is 64 bit and does support older 32 bit plug ins is that correct?

Just to make sure you have got it right from the links the others have posted already before...
Pro Tools 11 is 64bit but it DOES NOT support older 32bit plugins at all!

If you donīt want to upgrade your plugins to AAX 64bit versions or there are specific plugins
which are simply not available in this new format anymore, you better stay with PT10.

However there is kinda compromise you could make if you still would want to go with PT11.
All plugins or VIs which are available also in AU or VST 64bit you can use in Pro Tools 11
via host-plugins which are themselves AAX 64bit but can host other AU or VST 64bit plugins or VIs.

This is still the easiest and most affordable way to use older or not upgradable plugins in Pro Tools 11.
One thing that has to be mentioned, it is not the most convenient way in the long run though.

If so, I will buy PT 10. But which OSX runs PT 10 the most stable?
Lion, Mountain Lion or Mavericks?

As mentioned before you will have to buy the PT11+10 bundle anyway as PT10 isnīt available as a single license anymore.

If you now would go to install Mountain Lion 10.8.5 you actually could run both versions of Pro Tools on 1 computer.
Mountain Lion 10.8.5 was the latest Mac OS X version PT10 could be used with and is also one version of Mac OS
PT11 already can be used with.
Itīs the officially required Mac OS version no. by Avid for the use with the latest versions of both, PT10 and PT11
together one 1 computer.http://avid.force.com/pkb/articles/e...m-Requirements
...scroll down and click on "Mac OS Compatibility Grid" which will open a site with a very good, clear chart will
provide you all the needed info.